The Flux-Line Lattice in Superconductors

The Flux-Line Lattice in Superconductors

21 June 1995 | Ernst Helmut Brandt
The flux-line lattice (FLL) in superconductors consists of Abrikosov vortices, each carrying a quantum of magnetic flux, arranged in a triangular lattice. These vortices are pinned by material inhomogeneities and thermal fluctuations, especially in high-temperature superconductors (HTSCs). The FLL is described by Ginzburg-Landau (GL) theory and the London theory, which treat the vortex core as a singularity. In HTSCs, the FLL is soft due to large magnetic penetration depth and anisotropy, leading to enhanced softening and possible melting. Thermal fluctuations can cause thermally activated depinning of flux lines or "pancake vortices" in layers. Various phase transitions are predicted for the FLL in layered HTSCs. Despite large pinning forces and high critical currents, the small depinning energy limits the application of HTSCs as conductors at high temperatures. The FLL's elasticity is studied through moduli and line tension, while thermal fluctuations and melting are analyzed using Monte-Carlo simulations and phase transition criteria. In layered superconductors, 2D melting and Kosterlitz-Thouless transitions are observed, along with decoupling of layers and vortex fluctuations modifying magnetization. Flux motion involves various currents and dissipation mechanisms, while pinning is influenced by material defects and pinning forces. Thermally activated depinning is studied through models like the Kim-Anderson model and vortex-glass scaling. The paper summarizes the structure, properties, and behavior of the FLL in superconductors, highlighting its importance in understanding superconductivity and potential applications.The flux-line lattice (FLL) in superconductors consists of Abrikosov vortices, each carrying a quantum of magnetic flux, arranged in a triangular lattice. These vortices are pinned by material inhomogeneities and thermal fluctuations, especially in high-temperature superconductors (HTSCs). The FLL is described by Ginzburg-Landau (GL) theory and the London theory, which treat the vortex core as a singularity. In HTSCs, the FLL is soft due to large magnetic penetration depth and anisotropy, leading to enhanced softening and possible melting. Thermal fluctuations can cause thermally activated depinning of flux lines or "pancake vortices" in layers. Various phase transitions are predicted for the FLL in layered HTSCs. Despite large pinning forces and high critical currents, the small depinning energy limits the application of HTSCs as conductors at high temperatures. The FLL's elasticity is studied through moduli and line tension, while thermal fluctuations and melting are analyzed using Monte-Carlo simulations and phase transition criteria. In layered superconductors, 2D melting and Kosterlitz-Thouless transitions are observed, along with decoupling of layers and vortex fluctuations modifying magnetization. Flux motion involves various currents and dissipation mechanisms, while pinning is influenced by material defects and pinning forces. Thermally activated depinning is studied through models like the Kim-Anderson model and vortex-glass scaling. The paper summarizes the structure, properties, and behavior of the FLL in superconductors, highlighting its importance in understanding superconductivity and potential applications.
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